Can You Solve This Math Puzzle? The Trick Is in the Order of Operations

At first glance, this math puzzle looks almost too easy.

 

You see four 5s, a few simple symbols, and what appears to be a quick calculation. But there’s a small trick hiding in plain sight—and it has nothing to do with difficult math.

The challenge is:

5 + 5 + 5 ÷ 5

Can you solve it without falling for the trick?

Before you grab your calculator, take a second look. The way you approach the expression matters just as much as the numbers themselves!

Can You Solve It?

Here’s the puzzle one more time:

5 + 5 + 5 ÷ 5

What answer do you get?

Some people instinctively start calculating from the left:

• 5 + 5 = 10
• 10 + 5 = 15
• 15 ÷ 5 = 3

That gives you 3.

But there’s a problem.

That’s not the correct way to evaluate this expression.

The trick is hiding in the order of operations.

The Trick Is the Order of Operations

When a math expression contains several different operations, you can’t simply work from left to right.

Certain operations have priority over others.

In this puzzle, division must be performed before addition.

So instead of adding the first three 5s together, we first look at:

5 ÷ 5 = 1

Now replace that part of the expression:

5 + 5 + 1

And suddenly the rest is easy:

5 + 5 + 1 = 11

The correct answer is 11!

Why Isn’t the Answer 20?

Why Isn’t the Answer 20?

This is another little trap hidden in the puzzle.

You might look at the expression and immediately notice that it contains four 5s:

5 + 5 + 5 ÷ 5

That might make you think:

5 + 5 + 5 + 5 = 20

But that’s not what the expression says.

The last two 5s aren’t being added together.

They’re connected by a division symbol:

5 ÷ 5

And because division takes priority over addition, that part needs to be solved first.

So:

5 + 5 + 5 ÷ 5

becomes:

5 + 5 + 1

which gives:

11

That’s the little detail that makes this puzzle so easy to get wrong.

What Is the Order of Operations?

The order of operations is a set of rules that tells us which mathematical operations to perform first when an expression contains more than one type of operation.

A common way to remember it is PEMDAS:

• P — Parentheses
• E — Exponents
• M — Multiplication
• D — Division
• A — Addition
• S — Subtraction

So when you see multiplication or division mixed with addition or subtraction, don’t automatically calculate from left to right.

One Important Detail

There’s a detail about PEMDAS that’s worth remembering.

Multiplication and division have the same priority.

Likewise, addition and subtraction have the same priority.

When operations have equal priority, you generally work from left to right.

For example:

20 ÷ 5 × 2

You wouldn’t automatically multiply first just because multiplication appears in the PEMDAS acronym.

Instead:

20 ÷ 5 = 4

Then:

4 × 2 = 8

So the answer is 8.

The same left-to-right principle applies when addition and subtraction appear together.

Let’s Solve the Puzzle Step by Step

Now let’s go through the original expression slowly.

Step 1: Find the division

The expression is:

5 + 5 + 5 ÷ 5

The division is:

5 ÷ 5

Solve it:

5 ÷ 5 = 1

Step 2: Rewrite the expression

Now substitute 1 for 5 ÷ 5:

5 + 5 + 1

Step 3: Add the remaining numbers

Now there’s only addition:

5 + 5 + 1 = 11

And that’s it!

Final Answer: 11

No complicated calculation was needed.

The challenge was simply noticing which operation needed to be handled first.

Why This Puzzle Is So Easy to Misread

The numbers themselves are incredibly simple.

That’s what makes the puzzle effective.

When we see an expression made almost entirely from the same number, our brains can naturally group the numbers together. Seeing four 5s can make 20 feel like an obvious answer.

There’s also a tendency to read mathematical expressions the same way we read ordinary text—starting at the beginning and moving toward the end.

But math has its own set of rules.

The symbols matter.

In this case, that tiny ÷ sign completely changes how the expression needs to be approached.

A Quick Trick for Avoiding This Mistake

Before solving a mixed-operation expression, pause for a moment.

Instead of immediately calculating the first thing you see, scan the entire expression.

Ask yourself:

“Are there parentheses, exponents, multiplication, or division that need to be handled first?”

If the answer is yes, deal with those operations before moving on to addition or subtraction.

That one-second pause can save you from a surprisingly common mistake!

Can You Solve These Similar Expressions?

Now that you’ve spotted the trick, try these without looking at the answers.

Puzzle #1

10 + 10 ÷ 2

What do you get?

Don’t add the 10 + 10 first!

Puzzle #2

8 + 4 × 2

Remember that multiplication comes before addition.

Puzzle #3

20 − 8 ÷ 4

Look for the division before doing the subtraction.

Puzzle #4

6 + 6 ÷ 3 + 2

This one has more than one addition sign, but the same basic rule applies.

The fun part is seeing whether your brain automatically tries to calculate from left to right!

Frequently Asked Questions

What is the answer to 5 + 5 + 5 ÷ 5?

The correct answer is 11. First calculate 5 ÷ 5 = 1, then add 5 + 5 + 1.

Why isn’t the answer 20?

Because the final two 5s aren’t being added. They are connected by a division symbol, so 5 ÷ 5 must be calculated before the addition.

Why isn’t the answer 3?

The answer 3 comes from calculating the expression strictly from left to right. Mathematical order of operations requires the division to be completed before the addition.

What does PEMDAS stand for?

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

Do you always multiply before dividing?

No. Multiplication and division have the same priority. When both appear without parentheses, you generally work from left to right.

Do you always add before subtracting?

No. Addition and subtraction also have the same priority. When they appear together, work from left to right.

Is this puzzle actually difficult?

The arithmetic is very simple. The challenge comes from recognizing the correct order of operations rather than simply calculating from left to right.

The Final Answer

So, can you solve the puzzle without falling for the trick?

Absolutely!

Let’s see it one last time:

5 + 5 + 5 ÷ 5

First:

5 ÷ 5 = 1

Then:

5 + 5 + 1 = 11

The answer is 11!

Not 20.

Not 3.

11.

And that’s exactly why this little puzzle is so fun. The math is easy—the trick is remembering the rules!

Did You Get It Right?

Be honest…

Did you get 11 on your first try?

If you did, congratulations—you spotted the order-of-operations trick before it caught you.

And if you got a different answer, don’t feel bad. These simple-looking puzzles are designed to make you rush, and that’s often when our brains skip an important step.

Share this math puzzle with a friend or family member and see what answer they get.

Just don’t give away the trick first!

And if you enjoy quick brain teasers like this one, save it for the next time you’re in the mood for a little mathematical challenge.